A $$4 \times 1\,\,MUX$$ is used to implement a $$3$$- input Boolean function as shown in figure. The Boolean function $$F\left( {A,\,\,B,\,\,C} \right)$$ implemented is

The minimal product-of-sums function described by the $$K$$-map given in Fig.

The logic function $$F = AC + ABD + ACD$$ is to be realized using an $$8$$ to $$1$$ multiplexer shown in figure, using $$A, C$$ and $$D$$ as control inputs.

$$(a)$$ Indicate the inputs to be applied at the terminals $$0$$ to $$7.$$
$$(b)$$ Can the function be realize using a $$4$$ to $$1$$ multiplexer?
State YES or NO.

Match the following